A US source said: “In many respects you don’t need a memorial or service to remember David by...you have his music instead.

Home: David Bowie's apartment in New York (Image: splash)

"He would have wanted to just disappear with no fuss, no big show, no fan-fare. This would totally be his style.

"His last album Blackstar was very much his goodbye to fans instead.”

Bowie, who wasn’t religious, released the album to rave reviews on January 8 – his 69th birthday.

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On Monday, Bowie’s producer, Tony Visconti, wrote on Facebook that the album was his “parting gift” to fans.

“He always did what he wanted to do. And he wanted to do it his way and he wanted to do it the best way,” he said.

“His death was no different from his life - a work of art. He made Blackstar for us, his parting gift.”

Reclusive: The singer in one of his last public appearances (Image: Vantagenews.com)

The singer may have had what is known as a “direct cremation”, described on the New York State’s health department website as “the disposition of human remains by cremation without a formal viewing, visitation, or ceremony".

It is also variously described as one of the more affordable ways to dispose of someone who has passed away, costing between $700 to $900.

The deceased is generally collected from the place of death and transferred to the crematory. Once the required paperwork is done, they are then cremated.

Last wish: Bowie had told his family and friends of his plans (Image: Daily Mirror)

The remains are then generally returned to the family unless otherwise specified.

While Bowie has asked there not to be a public memorial to him, there are plans in place elsewhere, however, to honour his contribution to music.

There will be a tribute next month at the Brit Awards with the chairman Max Lousada saying: “Naturally, we wish to honour his extraordinary life and work at the forthcoming Brit awards and pay a fitting tribute to one of our greatest icons.”

Tributes: Fans and wellwishers gathered to pay their respects at a mural in South London (Image: Getty)

Bowie will also be honoured with a memorial concert at New York’s Carnegie Hall on March 31.

The concert to celebrate Bowie’s musical legacy was announced hours before his death and tickets sold out within hours.

Canadian indie rock band Arcade Fire , who collaborated closely with Bowie, also said in a statement: “David Bowie was one of the band’s earliest supporters and champions.

"He not only created the world that made it possible for our band to exist, he welcomed us into it with grace and warmth.

“We will take to the grave the moments we shared - talking, playing music and collaborating - as some of the most profound and memorable moments of our lives.”

Unforgettable: The star was smiling in what is thought to e one of the last pictures taken of him

Sir Elton John praised Bowie for dealing with his cancer battle with dignity.

He said: “What I loved about him towards the end was his incredible privacy during what must have been 10 years of incredible bad luck with illnesses, heart attacks, cancer, whatever.

"He kept it private in an age we’re living in with Twitter when everyone knows everything about everything - he kept it to himself.

Mourning: People pay tribute to Bowie at a memorial outside the apartment he shared with Iman in New York (Image: Getty)

"He made two albums without anybody knowing he was making them. He had treatment for his illnesses without anyone knowing or anyone saying anything.

"And that is the mystique of the man, because we know David Bowie the figure, the singer, the outrageous performer, but actually, we don’t know anything about him - and that’s the way it should be in music and should be in any art form whatsoever.”

Meanwhile, one of Bowie’s closest aides told how it was almost as if the singer knew he was going to die two days after his birthday.